How many distinct 5 digit numbers can be formed using the digits … - Vidyadip

Question

How many distinct 5 digit numbers can be formed using the digits 3, 2, 3, 2, 4, 5.

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Answer

5 digit numbers are to be formed from 2, 3, 2, 3, 4, 5. Case I: Numbers formed from 2, 2, 3, 4, 5 OR 2, 3, 3, 4, 5

Number of such numbers $=\frac{5 !}{2 !}+\frac{5 !}{2 !}=5 !=120$

Case II: Numbers are formed from 2, 2, 3, 3 and any one of 4 or 5

Number of such numbers $=\frac{5 !}{2 ! 2 !}+\frac{5 !}{2 ! 2 !}=60$

Required number of numbers = 120 + 60 = 180

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